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XXXIII. Intelligence and Miscellaneous Articles. 



ON THE THEORY OF THE OSCILLATORY DISCHARGE. 

 BY PROF. J. STEFAN. 



HPHE theory of the oscillatory discharge of a Leyden jar has been 

 -*- developed by Sir William Thomson and Kircbhoff. It gives for 

 the intensity of the current of the discharge an equation which 

 agrees with that for the motion of a pendulum in a resisting 

 medium. In developing the theory it was assumed that the 

 discharge-current fills the entire section of the discharging wire 

 with uniform density. With very rapidly succeeding currents this 

 supposition is far from the reality. In such cases the motion of 

 the electricity in metallic conductors is almost entirely restricted 

 to a thin layer on the surface of the conductor. 



The theory may be developed by taking into account this unequal 

 division of the current. The result is essentially that an oscilla- 

 tory discharge is always made up of two motions, one of which is 

 extinguished much earlier than the other. It is the latter which, 

 as the time increases, acquires the character of a pendulum motion. 

 The amplitudes diminish, however, much more rapidly according 

 to the new theory than according to the old one. 



In so far as the influence of the resistance on the time of oscil- 

 lation of this motion is small, the new theory gives a formula for 

 "it analogous with the earlier one, excepting that, instead of the 

 coefficient of self-induction of the wire, we have that of the induc- 

 tion on a filament in the surface. In consequence of this the time 

 of vibration is independent of the magnetic condition of the dis- 

 charging wire, and is therefore almost as large for an iron wire as 

 for a copper one, while according to the older theory it is found to 

 be many times greater for the former. 



The interposition of a break in the circuit might cause a still 

 greater deviation from the pendulum motion than that indicated 

 by theory. Such a deviation has the effect that the discharge- 

 circuit on a conductor connected with it also induces electrical 

 movements in another, even when the time of vibration of the 

 latter is quite different from the time of oscillation of the exciting 

 discharge, and when therefore a true resonance is excluded. 



This motion experiences also an increase if the induction-impulse 

 is repeated in a favourable time, that is in one corresponding to 

 the special vibrations of the conductor, for instance in consequence 

 of a reflexion at the end of the inducing wire. The observations 

 made by Sarasin and De la Rive may be referred to this. 



Electricity in motion shows much more markedly than in other 

 phenomena the property of inertia. This discharge is often com- 

 pared with the oscillations of a liquid in two communicating tubes. 

 Such a comparison affords only an image of the phenomenon which 

 is difficult of observation. A wider significance may, however, be 

 ascribed to it. The energy which corresponds to the difference in 



